Another reason sinusoids are important is that they are
eigenfunctions of linear systems (which we'll say more about in
§4.1.4). This means that they are important in the analysis
of filters such as reverberators, equalizers, certain (but not
all) ``audio effects'', etc.

Perhaps most importantly, from the point of view of computer music
research, is that the human ear is a kind of spectrum
analyzer. That is, the cochlea of the inner ear physically splits
sound into its (quasi) sinusoidal components. This is accomplished by
the basilar membrane in the inner ear: a sound wave injected at
the oval window (which is connected via the bones of the middle
ear to the ear drum), travels along the basilar membrane inside
the coiled cochlea. The membrane starts out thick and stiff, and
gradually becomes thinner and more compliant toward its apex (the
helicotrema). A stiff membrane has a high resonance frequency
while a thin, compliant membrane has a low resonance frequency
(assuming comparable mass per unit length, or at least less of a
difference in mass than in compliance). Thus, as the sound wave
travels, each frequency in the sound resonates at a particular
place along the basilar membrane. The highest audible frequencies
resonate right at the entrance, while the lowest frequencies travel
the farthest and resonate near the helicotrema. The membrane
resonance effectively ``shorts out'' the signal energy at the resonant
frequency, and it travels no further. Along the basilar membrane
there are hair cells which ``feel'' the resonant vibration and
transmit an increased firing rate along the auditory nerve to the
brain. Thus, the ear is very literally a Fourier analyzer for sound,
albeit nonlinear and using ``analysis'' parameters that are difficult
to match exactly. Nevertheless, by looking at spectra (which display
the amount of each sinusoidal frequency present in a sound), we are
looking at a representation much more like what the brain receives
when we hear.